Transcendence conjectures about periods of modular forms and rational structures on spaces of modular forms
The conjecture is made that the rational structures on spaces of modular forms coming from the rationality of Fourier coefficients and the rationality of periods are not compatible. A consequence would be that ζ(2k-1)/π 2k-1 (ζ(s)=Riemann zeta function;k∈ℕ,k≥2) is irrational or even transcendental.
KeywordsModular forms rational structures periods transcendence Riemann zeta function
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